Letter from American the BBC occasionally sent up (4)
I believe the answer is:
beta
'letter' is the definition.
(beta is a kind of letter of the alphabet)
'american the bbc occasionally sent up' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'occasionally' indicates alternate letters (letters taken at regular intervals or occasions).
'sent up' says the letters should be written backwards.
'the'+'bbc'='thebbc'
The alternate letters of 'thebbc' are 'teb'.
'a'+'teb'='ateb'
'ateb' back-to-front is 'BETA'.
'from' is the link.
(Other definitions for beta that I've seen before include "second class grade?" , "Second Greek letter, B" , "Letter before gamma" , "Second-rate" , "Second-class" .)